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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education
*8317846402*
0581/33
MATHEMATICS
Paper 3 (Core)
October/November 2013
2 hours
Candidates answer on the Question Paper.
Additional Materials:
Electronic calculator
Tracing paper (optional)
Geometrical instruments
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.
Write in dark blue or black pen.
You may use a pencil for any diagrams or graphs.
Do not use staples, paper clips, highlighters, glue or correction fluid.
DO NOT WRITE IN ANY BARCODES.
Answer all questions.
If working is needed for any question it must be shown below that question.
Electronic calculators should be used.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to
three significant figures. Give answers in degrees to one decimal place.
For π, use either your calculator value or 3.142.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total of the marks for this paper is 104.
This document consists of 16 printed pages.
IB13 11_0581_33/FP
© UCLES 2013
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1
For
Examiner′s
Use
Adam owns a farm.
(a) He plans to keep twenty hens.
He works out what he thinks this will cost.
Complete the following table.
Item
Cost ($)
Equipment
500
20 hens costing $12 each
3 years supply of feed
costing $25 per month
TOTAL
[3]
(b) The equipment actually costs $600.
The ratio of costs is
equipment : hens : feed = 5 : 3 : 9 .
(i) Show that the total cost is now $2040.
Answer(b)(i)
[2]
(ii) Adam actually buys more than 20 hens, each costing $12.
How many hens does he buy?
Answer(b)(ii) ............................................... [2]
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(c) Adam makes $2920 from selling his hens’ eggs.
Calculate his percentage profit on the $2040.
Answer(c) ........................................... % [2]
(d) Adam borrows $1500 for 3 years at a rate of 5.5% per year compound interest.
Calculate the interest he will pay, correct to the nearest cent.
Answer(d) $ ................................................ [3]
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© UCLES 2013
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2
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Examiner′s
Use
The diagram shows four quadrilaterals drawn on a 1 cm2 grid.
y
8
7
X
6
5
A
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1 0
x
1
2
3
4
5
6
7
8
–1
–2
–3
B
C
–4
–5
–6
–7
–8
(a) Write down the mathematical name of the quadrilateral X.
Answer(a) ............................................... [1]
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(b) Describe fully the single transformation that maps quadrilateral X onto quadrilateral
(i) A,
Answer(b)(i) ......................................................................................................................
........................................................................................................................................... [3]
(ii) B,
Answer(b)(ii) .....................................................................................................................
........................................................................................................................................... [2]
(iii) C.
Answer(b)(iii) ....................................................................................................................
........................................................................................................................................... [3]
(c) (i) Calculate the length of the longest side of quadrilateral X.
Show that your answer rounds to 3.16 cm, correct to 3 significant figures.
Answer(c)(i)
[2]
(ii) Calculate the perimeter of quadrilateral X.
Answer(c)(ii) ......................................... cm [3]
(iii) Find the perimeter of quadrilateral C.
Answer(c)(iii) ......................................... cm [1]
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(a) Using only the integers from 1 to 50, find
(i) a multiple of both 4 and 7,
Answer(a)(i) ............................................... [1]
(ii) a square number that is odd,
Answer(a)(ii) ............................................... [1]
(iii) an even prime number,
Answer(a)(iii) ............................................... [1]
(iv) a prime number which is one less than a multiple of 5.
Answer(a)(iv) ............................................... [1]
(b) Find the value of
2
(i) ^ 5 h ,
Answer(b)(i) ............................................... [1]
(ii) 2–3 × 63.
Answer(b)(ii) ............................................... [2]
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(a) A regular polygon has 9 sides.
For this polygon, calculate
(i) the size of one exterior angle,
Answer(a)(i) ............................................... [2]
(ii) the size of one interior angle.
Answer(a)(ii) ............................................... [1]
(b)
C
w°
24°
y°
B
NOT TO
SCALE
D
O
E
z° x°
A
F
In the diagram, A, B, C and D are points on the circumference of a circle, centre O.
AB is the diameter and EF is a tangent to the circle at A.
AB is parallel to DC and angle ACD = 24°.
Find
(i) w,
Answer(b)(i) w = ............................................... [1]
(ii) x,
Answer(b)(ii) x = ............................................... [1]
(iii) y.
Answer(b)(iii) y = ............................................... [1]
(c) Complete the statement.
z = ............................... because ................................................................................................
................................................................................................................................................... [2]
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Examiner′s
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(a) (i) Complete the table for y = 5 + 3x – x2.
x
–2
y
–5
–1
0
1
5
7
2
3
4
5
5
–5
[3]
y = 5 + 3x – x2 for –2 Y x Y 5.
(ii) On the grid, draw the graph of
y
8
7
6
5
4
3
2
1
–2
–1
0
1
2
3
4
5
x
–1
–2
–3
–4
–5
–6
[4]
(b) Use your graph to solve the equation 5 + 3x – x2 = 0 .
Answer(b) x = ..................... or x = ..................... [2]
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(c) (i) On the grid, draw the line of symmetry of y = 5 + 3x – x2.
[1]
For
Examiner′s
Use
(ii) Write down the equation of this line of symmetry.
Answer(c)(ii) ............................................... [1]
(d) (i) On the grid, draw a straight line from (–1, 1) to (3, 5).
[1]
(ii) Work out the gradient of this line.
Answer(d)(ii) ............................................... [2]
(iii) Write down the equation of this line in the form y = mx + c.
Answer(d)(iii) y = ............................................... [1]
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© UCLES 2013
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6
For
Examiner′s
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Alison scored the following number of runs in 15 cricket matches.
12
3
27
35
0
7
52
4
18
30
18
7
94
61
7
(a) For these scores,
(i) work out the median,
Answer(a)(i) ............................................... [2]
(ii) write down the mode,
Answer(a)(ii) ............................................... [1]
(iii) calculate the mean.
Answer(a)(iii) ............................................... [2]
(b) These are the averages for the number of runs scored by Bethan in the 15 matches.
Median = 21
Mode = 13
Mean = 20
Alison says that her scores are better than Bethan’s scores.
Bethan says that her scores are better than Alison’s scores.
Explain how they could both be correct.
Answer(b) .................................................................................................................................
...................................................................................................................................................
................................................................................................................................................... [2]
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(c) Alison puts her 15 scores into 4 groups and shows them in a pie chart.
(i) Complete the table.
Score
Frequency
Sector Angle
0 to 25
9
216°
26 to 50
51 to 75
76 to 100
[3]
(ii) Complete the pie chart and label the sectors.
0 to 25
[3]
(d) Estimate the probability that in the next match Alison will score more than 25 runs.
Give your answer as a fraction in its simplest form.
Answer(d) ............................................... [2]
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7
D
C
E
NOT TO
SCALE
2.25 m
1.5 m
A
B
1.0 m
The diagram shows a trapezium ABCD.
AB = 1.0 m, AD = 2.25 m, BC = 1.5 m and angle DEC = 90°.
(a) Using trigonometry, calculate angle DCE.
Answer(a) Angle DCE = ............................................... [3]
(b) Calculate the area of the trapezium ABCD.
Answer(b) .......................................... m2 [2]
(c) ABCD is the cross-section of a box.
The box is 2 m long.
Calculate the volume of the box.
D
2m
C
B
A
Answer(c) .......................................... m3 [1]
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(d) On the grid, complete the net of the box.
The base and one face of the box have been drawn for you.
The scale is 2 cm to 1 m.
[4]
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Examiner′s
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Here is a sequence of patterns made using identical polygons.
Pattern 1
Pattern 2
Pattern 3
(a) Write down the mathematical name of the polygon in Pattern 1.
Answer(a) ............................................... [1]
(b) Complete the table for the number of vertices (corners) and the number of lines in Pattern 3,
Pattern 4 and Pattern 7.
Pattern
1
2
Number of vertices
8
14
Number of lines
8
15
3
4
7
[5]
(c) (i) Find an expression for the number of vertices in Pattern n.
Answer(c)(i) ............................................... [2]
(ii) Work out the number of vertices in Pattern 23.
Answer(c)(ii) ............................................... [1]
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(d) Find an expression for the number of lines in Pattern n.
Answer(d) ............................................... [2]
(e) Work out an expression, in its simplest form, for
(number of lines in Pattern n) – (number of vertices in Pattern n).
Answer(e) ............................................... [2]
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Question 9 is printed on the next page.
© UCLES 2013
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1
(a) The formula for the volume, V, of a cone with radius r, and height h, is V = 3 πr2h .
(i) To make r the subject of this formula, the first step is 3V = πr2h.
Show the remaining steps to make r the subject of this formula.
Answer(a)(i) r = ............................................... [2]
(ii) An ice-cream cone has a volume of 141 cm3 and height 15 cm.
Show that the radius of the cone is 3 cm, correct to the nearest whole number.
Answer(a)(ii)
[2]
(b) The open end of an ice-cream cone is a circle of radius 3 cm.
Calculate the circumference of this circle.
Answer(b) ......................................... cm [2]
(c) The volume of a ball of ice-cream is 113 cm3.
The ball of ice-cream costs $2.15 .
Calculate the cost of 1 cm3 of the ice-cream.
Give your answer in cents, correct to 1 decimal place.
Answer(c) ...................................... cents [3]
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reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included the
publisher will be pleased to make amends at the earliest possible opportunity.
University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of
Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2013
0581/33/O/N/13